Journal of Function Spaces http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2016 , Hindawi Publishing Corporation . All rights reserved. Fixed Point Theorems for Cyclic Contractions in -Algebra-Valued -Metric Spaces Thu, 11 Feb 2016 12:54:26 +0000 http://www.hindawi.com/journals/jfs/2016/7827040/ We study fundamental properties of -algebra-valued -metric space which was introduced by Ma and Jiang (2015) and give some fixed point theorems for cyclic mapping with contractive and expansive condition on such space analogous to the results presented in Ma and Jiang, 2015. Chakkrid Klin-eam and Prondanai Kaskasem Copyright © 2016 Chakkrid Klin-eam and Prondanai Kaskasem. All rights reserved. On Coupled Common Fixed Point Theorems for Nonlinear Contractions with the Mixed Weakly Monotone Property in Partially Ordered -Metric Spaces Sun, 07 Feb 2016 08:10:29 +0000 http://www.hindawi.com/journals/jfs/2016/7529523/ The main aim of this paper is to establish some coupled common fixed point theorems under a Geraghty-type contraction using mixed weakly monotone property in partially ordered -metric space. Also, we give some sufficient conditions for the uniqueness of a coupled common fixed point. Some examples are provided to demonstrate the validity of our results. Mi Zhou and Xiao-Lan Liu Copyright © 2016 Mi Zhou and Xiao-Lan Liu. All rights reserved. On a Kantorovich Variant of -Szász-Mirakjan Operators Wed, 03 Feb 2016 12:10:36 +0000 http://www.hindawi.com/journals/jfs/2016/1035253/ We propose a Kantorovich variant of -analogue of Szász-Mirakjan operators. We establish the moments of the operators with the help of a recurrence relation that we have derived and then prove the basic convergence theorem. Next, the local approximation and weighted approximation properties of these new operators in terms of modulus of continuity are studied. M. Mursaleen, Abdullah Alotaibi, and Khursheed J. Ansari Copyright © 2016 M. Mursaleen et al. All rights reserved. Optimal Bounds for Neuman Mean Using Arithmetic and Centroidal Means Tue, 02 Feb 2016 09:34:02 +0000 http://www.hindawi.com/journals/jfs/2016/5131907/ We present the best possible parameters and such that the double inequalities and hold for all with and give several sharp inequalities involving the hyperbolic and inverse hyperbolic functions. Here, , , , and are, respectively, the Neuman, arithmetic, quadratic, and centroidal means of and , and . Ying-Qing Song, Wei-Mao Qian, and Yu-Ming Chu Copyright © 2016 Ying-Qing Song et al. All rights reserved. Iterative Approximations for Zeros of Sum of Accretive Operators in Banach Spaces Sun, 31 Jan 2016 15:47:21 +0000 http://www.hindawi.com/journals/jfs/2016/5973468/ We study the approximation of zero for sum of accretive operators using a modified Mann type forward-backward splitting algorithm and obtain strong convergence of the sequence generated by our scheme to the zero of sum of accretive operators in uniformly convex real Banach spaces which are also uniformly smooth. Our result is new and complements many recent and important results in this direction in the literature. Yekini Shehu Copyright © 2016 Yekini Shehu. All rights reserved. Subclasses of Analytic Functions Defined by Generalized Hypergeometric Functions Sun, 31 Jan 2016 12:25:42 +0000 http://www.hindawi.com/journals/jfs/2016/7390410/ We introduce a new subclass of analytic functions in the unit disk , defined by using the generalized hypergeometric functions, which extends some previous well-known classes defined by different authors. Inclusion results, radius problems, and some connections with the Bernardi-Libera-Livingston integral operator are discussed. Badr S. Alkahtani, Saima Mustafa, and Teodor Bulboacă Copyright © 2016 Badr S. Alkahtani et al. All rights reserved. Hamilton-Souplet-Zhang’s Gradient Estimates for Two Types of Nonlinear Parabolic Equations under the Ricci Flow Thu, 28 Jan 2016 11:03:50 +0000 http://www.hindawi.com/journals/jfs/2016/2894207/ We consider gradient estimates for two types of nonlinear parabolic equations under the Ricci flow: one is the equation with being two real constants; the other is with being two real constants. By a suitable scaling for the above two equations, we obtain Hamilton-Souplet-Zhang-type gradient estimates. Guangyue Huang and Bingqing Ma Copyright © 2016 Guangyue Huang and Bingqing Ma. All rights reserved. Continuity Results and Error Bounds on Pseudomonotone Vector Variational Inequalities via Scalarization Thu, 28 Jan 2016 10:40:49 +0000 http://www.hindawi.com/journals/jfs/2016/7297854/ Continuity (both lower and upper semicontinuities) results of the Pareto/efficient solution mapping for a parametric vector variational inequality with a polyhedral constraint set are established via scalarization approaches, within the framework of strict pseudomonotonicity assumptions. As a direct application, the continuity of the solution mapping to a parametric weak Minty vector variational inequality is also discussed. Furthermore, error bounds for the weak vector variational inequality in terms of two known regularized gap functions are also obtained, under strong pseudomonotonicity assumptions. Xin Zuo, Hong-Zhi Wei, and Chun-Rong Chen Copyright © 2016 Xin Zuo et al. All rights reserved. A Remark on the Stability of Approximative Compactness Thu, 21 Jan 2016 14:27:14 +0000 http://www.hindawi.com/journals/jfs/2016/2734947/ We study the stability of approximative -compactness, where is the norm or the weak topology. Let be an index set and for every let be a subspace of a Banach space . For , let and . We prove that (resp., ) is approximatively -compact in if and only if, for every , (resp., ) is approximatively -compact in . Zhenghua Luo, Longfa Sun, and Wen Zhang Copyright © 2016 Zhenghua Luo et al. All rights reserved. Properties of Commutativity of Dual Toeplitz Operators on the Orthogonal Complement of Pluriharmonic Dirichlet Space over the Ball Wed, 20 Jan 2016 12:52:51 +0000 http://www.hindawi.com/journals/jfs/2016/1054768/ We completely characterize the pluriharmonic symbols for (semi)commuting dual Toeplitz operators on the orthogonal complement of the pluriharmonic Dirichlet space in Sobolev space of the unit ball. We show that, for and pluriharmonic functions, on if and only if and satisfy one of the following conditions: both and are holomorphic; both and are holomorphic; there are constants and , both not being zero, such that is constant. Yinyin Hu, Yufeng Lu, and Tao Yu Copyright © 2016 Yinyin Hu et al. All rights reserved. A Sharp Lower Bound for Toader-Qi Mean with Applications Sun, 17 Jan 2016 13:52:59 +0000 http://www.hindawi.com/journals/jfs/2016/4165601/ We prove that the inequality holds for all with if and only if , where , , and are, respectively, the Toader-Qi and -order logarithmic means of and . As applications, we find two fine inequalities chains for certain bivariate means. Zhen-Hang Yang and Yu-Ming Chu Copyright © 2016 Zhen-Hang Yang and Yu-Ming Chu. All rights reserved. On Coupled Systems of Time-Fractional Differential Problems by Using a New Fractional Derivative Mon, 04 Jan 2016 07:39:47 +0000 http://www.hindawi.com/journals/jfs/2016/4626940/ The existence of solutions for a coupled system of time-fractional differential equations including continuous functions and the Caputo-Fabrizio fractional derivative is examined. After that we investigated a coupled system of time-fractional differential inclusions including compact- and convex-valued -Caratheodory multifunctions and the Caputo-Fabrizio fractional derivative. Ahmed Alsaedi, Dumitru Baleanu, Sina Etemad, and Shahram Rezapour Copyright © 2016 Ahmed Alsaedi et al. All rights reserved. On Probabilistic Alpha-Fuzzy Fixed Points and Related Convergence Results in Probabilistic Metric and Menger Spaces under Some Pompeiu-Hausdorff-Like Probabilistic Contractive Conditions Thu, 31 Dec 2015 14:03:32 +0000 http://www.hindawi.com/journals/jfs/2015/213174/ In the framework of complete probabilistic metric spaces and, in particular, in probabilistic Menger spaces, this paper investigates some relevant properties of convergence of sequences to probabilistic α-fuzzy fixed points under some types of probabilistic contractive conditions. M. De la Sen Copyright © 2015 M. De la Sen. All rights reserved. Sandor Type Inequalities for Sugeno Integral with respect to General -Convex Functions Wed, 30 Dec 2015 12:54:41 +0000 http://www.hindawi.com/journals/jfs/2015/460520/ The concept for general -convex functions, as a generalization of convex functions, is introduced. Then, Sandor type inequalities for the Sugeno integral based on this kind of function are established. Our work generalizes the previous results in the literature. Finally, some conclusions and problems for further investigations are given. Dong-Qing Li, Yu-Hu Cheng, and Xue-Song Wang Copyright © 2015 Dong-Qing Li et al. All rights reserved. New Applications of Nunokawa’s Lemmas Mon, 28 Dec 2015 13:08:30 +0000 http://www.hindawi.com/journals/jfs/2015/241264/ We derive several univalent and -valent conditions on certain meromorphic functions by applying well-known Nunokawa’s lemmas. Yi-Hui Xu and Jin-Lin Liu Copyright © 2015 Yi-Hui Xu and Jin-Lin Liu. All rights reserved. Boundedness of Commutators of Marcinkiewicz Integrals on Nonhomogeneous Metric Measure Spaces Tue, 22 Dec 2015 06:46:54 +0000 http://www.hindawi.com/journals/jfs/2015/548165/ Let be a metric measure space satisfying the upper doubling condition and geometrically doubling condition in the sense of Hytönen. The aim of this paper is to establish the boundedness of commutator generated by the Marcinkiewicz integral and Lipschitz function . The authors prove that is bounded from the Lebesgue spaces to weak Lebesgue spaces for , from the Lebesgue spaces to the spaces for , and from the Lebesgue spaces to the Lipschitz spaces for . Moreover, some results in Morrey spaces and Hardy spaces are also discussed. Guanghui Lu and Shuangping Tao Copyright © 2015 Guanghui Lu and Shuangping Tao. All rights reserved. On Geodesic Segments in the Infinitesimal Asymptotic Teichmüller Spaces Sun, 20 Dec 2015 09:18:14 +0000 http://www.hindawi.com/journals/jfs/2015/276719/ Let be the infinitesimal asymptotic Teichmüller space of a Riemann surface of infinite type. It is known that is the quotient Banach space of the infinitesimal Teichmüller space , where is the dual space of integrable quadratic differentials. The purpose of this paper is to study the nonuniqueness of geodesic segment joining two points in . We prove that there exist infinitely many geodesic segments between the basepoint and every nonsubstantial point in the universal infinitesimal asymptotic Teichmüller space by constructing a special degenerating sequence. Yan Wu, Yi Qi, and Zunwei Fu Copyright © 2015 Yan Wu et al. All rights reserved. Some New Results on Fixed Points of Meromorphic Functions Defined in Annuli Thu, 17 Dec 2015 09:59:48 +0000 http://www.hindawi.com/journals/jfs/2015/426576/ The purpose of this paper is to investigate the fixed points of meromorphic functions in annuli. Some well-known facts of fixed points for meromorphic functions in the plane will be considered in annuli. Zhaojun Wu, Zuxing Xuan, and Yuxian Chen Copyright © 2015 Zhaojun Wu et al. All rights reserved. An Existence Result of Positive Solutions for Fully Second-Order Boundary Value Problems Wed, 16 Dec 2015 07:17:03 +0000 http://www.hindawi.com/journals/jfs/2015/287253/ An existence result of positive solutions is obtained for the fully second-order boundary value problem       where is continuous. The nonlinearity may be sign-changing and superlinear growth on and . Our discussion is based on the method of lower and upper solution. Yongxiang Li and Yaya Shang Copyright © 2015 Yongxiang Li and Yaya Shang. All rights reserved. Existence and Continuous Dependence for Fractional Partial Hyperbolic Differential Equations Tue, 15 Dec 2015 08:46:42 +0000 http://www.hindawi.com/journals/jfs/2015/875170/ This paper is concerned with a class of fractional hyperbolic partial differential equations with the Caputo derivative. Existence and continuous dependence results of solutions are obtained under the hypothesis of the Lipschitz condition without any restriction on the Lipschitz constant. Examples are discussed to illustrate the results. Qixiang Dong, Guangxian Wu, and Lanping Zhu Copyright © 2015 Qixiang Dong et al. All rights reserved. Existence of Solutions for Degenerate Elliptic Problems in Weighted Sobolev Space Wed, 02 Dec 2015 12:46:49 +0000 http://www.hindawi.com/journals/jfs/2015/265127/ This paper is devoted to the study of the existence of solutions to a general elliptic problem , with and , where is a Leray-Lions operator from a weighted Sobolev space into its dual and is a nonlinear term satisfying , , and a growth condition with respect to . Here, , are weight functions that will be defined in the Preliminaries. Lili Dai, Wenjie Gao, and Zhongqing Li Copyright © 2015 Lili Dai et al. All rights reserved. Hyers-Ulam Stability of the First-Order Matrix Differential Equations Mon, 30 Nov 2015 08:26:39 +0000 http://www.hindawi.com/journals/jfs/2015/614745/ We prove the generalized Hyers-Ulam stability of the first-order linear homogeneous matrix differential equations . Moreover, we apply this result to prove the generalized Hyers-Ulam stability of the th order linear differential equations with variable coefficients. Soon-Mo Jung Copyright © 2015 Soon-Mo Jung. All rights reserved. The Boundedness of Some Integral Operators on Weighted Hardy Spaces Associated with Schrödinger Operators Wed, 25 Nov 2015 14:07:30 +0000 http://www.hindawi.com/journals/jfs/2015/823862/ Let be a Schrödinger operator acting on , , where is a nonnegative locally integrable function on . In this paper, we will first define molecules for weighted Hardy spaces associated with and establish their molecular characterizations. Then, by using the atomic decomposition and molecular characterization of , we will show that the imaginary power is bounded on for , and the fractional integral operator is bounded from to , where , , and . Hua Wang Copyright © 2015 Hua Wang. All rights reserved. Lebesgue Decomposition Theorem and Weak Radon-Nikodým Theorem for Generalized Fuzzy Number Measures Wed, 25 Nov 2015 05:34:17 +0000 http://www.hindawi.com/journals/jfs/2015/576134/ The Lebesgue type decomposition theorem and weak Radon-Nikodým theorem for fuzzy valued measures in separable Banach spaces are established. Cai-Li Zhou and Fu-Gui Shi Copyright © 2015 Cai-Li Zhou and Fu-Gui Shi. All rights reserved. Necessary and Sufficient Conditions for Inner Functions to Be in -Spaces Tue, 24 Nov 2015 07:51:48 +0000 http://www.hindawi.com/journals/jfs/2015/376089/ Under some regularity conditions on , inner functions in -spaces are characterized in the following way: an inner function belongs to if and only if it is a Blaschke product associated with satisfying , where . The result generalizes earlier theorems in (Essén et al., 2006) and (Pérez-González and Rättyä, 2009). Atte Reijonen Copyright © 2015 Atte Reijonen. All rights reserved. Topological Structures of Derivative Weighted Composition Operators on the Bergman Space Wed, 18 Nov 2015 08:30:00 +0000 http://www.hindawi.com/journals/jfs/2015/672385/ We characterize the difference of derivative weighted composition operators on the Bergman space in the unit disk and determine when linear-fractional derivative weighted composition operators belong to the same component of the space of derivative weighted composition operators on the Bergman space under the operator norm topology. Ce-Zhong Tong, Cheng Yuan, and Ze-Hua Zhou Copyright © 2015 Ce-Zhong Tong et al. All rights reserved. Categories of -Fuzzy Greedoids Tue, 10 Nov 2015 07:34:07 +0000 http://www.hindawi.com/journals/jfs/2015/543247/ The concepts of -greedoids, fuzzifying greedoids, and ()-fuzzy greedoids are introduced and feasibility preserving mappings between greedoids are defined. Then -feasibility preserving mappings, fuzzifying feasibility preserving mappings, and ()-fuzzy feasibility preserving mappings are given as generalizations of feasibility preserving mappings. We study the relations among greedoids, -greedoids, fuzzifying greedoids, and ()-fuzzy greedoids from a categorical point of view. Zhen-Yu Xiu and Fu-Gui Shi Copyright © 2015 Zhen-Yu Xiu and Fu-Gui Shi. All rights reserved. The Randomized American Option as a Classical Solution to the Penalized Problem Tue, 27 Oct 2015 08:11:12 +0000 http://www.hindawi.com/journals/jfs/2015/245436/ We connect the exercisability randomized American option to the penalty method by showing that the randomized American option value is the unique classical solution to the Cauchy problem corresponding to the canonical penalty problem for American options. We also establish a uniform bound for , where is the infinitesimal generator of a geometric Brownian motion. Guillaume Leduc Copyright © 2015 Guillaume Leduc. All rights reserved. Formulae for the Generalized Drazin Inverse of a Block Matrix in Banach Algebras Wed, 21 Oct 2015 12:18:34 +0000 http://www.hindawi.com/journals/jfs/2015/767568/ We present some new representations for the generalized Drazin inverse of a block matrix in a Banach algebra under conditions weaker than those used in resent papers on the subject. Xiaoji Liu and Xiaolan Qin Copyright © 2015 Xiaoji Liu and Xiaolan Qin. All rights reserved. Convergence Theorems for Generalized Functional Sequences of Discrete-Time Normal Martingales Thu, 15 Oct 2015 12:13:34 +0000 http://www.hindawi.com/journals/jfs/2015/360679/ The Fock transform recently introduced by the authors in a previous paper is applied to investigate convergence of generalized functional sequences of a discrete-time normal martingale . A necessary and sufficient condition in terms of the Fock transform is obtained for such a sequence to be strongly convergent. A type of generalized martingales associated with is introduced and their convergence theorems are established. Some applications are also shown. Caishi Wang and Jinshu Chen Copyright © 2015 Caishi Wang and Jinshu Chen. All rights reserved.